A variety of optical metrology techniques have been developed for non-contact mapping in three dimensions of the surface profile and shape of objects and their subsequent conversion into digital data. Techniques based on optical triangulation have found a widespread use and they are currently implemented in three-dimensional (3D) optical mapping (profiler) instruments available from various vendors. A popular type of triangulation-based 3D profiler instruments, sometimes referred to as slit scanners, includes a light projector that projects a fan-shaped illumination light beam on the surface of the object to be mapped.
In accordance with the principle of optical trigonometric triangulation, a camera captures images of the luminous line formed on the object by the light beam. A large portion of an object can be mapped by capturing a set of images at a suitable frame rate while the object is translated relative to the projected fan-shaped light beam. Alternatively, the object can be kept immobile while the projected light beam is swept over the object along a direction perpendicular to the luminous line.
Depending on factors such as the width of the fan-shaped light beam illuminating the object, the magnification of the camera objective lens and the size of the photosensitive elements (pixels) of the image sensor of the camera, the digital images of the luminous line will not be infinitely thin, their minimum widths being ultimately limited by the size of each individual pixel of the image sensor. Note that the term “width” refers herein to the smallest dimension (thickness) of the luminous line, the other dimension being referred to as the line length. One processing step in high-resolution optical 3D profiling is the determination of the centerline in the image of each luminous line. The expression “centerline” is understood herein to refer to the imaginary, infinitely-thin continuous line constructed from the succession of points that pass through the “center” of the width of an imaged luminous line. Various methods can be used for computing the centerline of an imaged luminous line, one of the most popular being the computation of the first moment (also referred to as the center of gravity, the center of mass or the centroid) of the brightness (irradiance) profile along the width of the line.
In this regard, it should be noted that the brightness of the image of a luminous line is neither perfectly uniform along the width of the line nor bounded by well-defined, steep edges. In fact, the brightness along this direction is generally better described by the well-known bell-shaped Gaussian function, which is largely determined by the typically Gaussian irradiance profile along the width of the fan-shaped light beam that illuminates the object. Ideally, the brightness variations along the width of a line would resemble to a smooth, symmetrical Gaussian profile having a well-defined center peak value that can serve to define the centerline at any position along the length of the imaged line. Likewise, this ideal situation means that the Gaussian brightness profile would be wide enough to cover several pixels of the image sensor anywhere along the length of the imaged line. Unfortunately, in real-life situations the Gaussian-shaped line brightness often appears as more or less distorted, leading to difficulties in determining the centerline, and then to surface profiling of an object with reduced accuracy.
A source of distortions in the otherwise Gaussian-shaped brightness profile along the width of the imaged luminous line originates from fine-pitch (small-scale) variations of the optical reflectance characteristics (also known as the texture) of the object's surface that occur on a scale that compares to the width of the fan-shaped illumination light beam in the plane of the object. These variations in the reflectance of the object's surface can corrupt the optical irradiance distribution of the light reflected by the surface and then captured by the camera objective lens to form the image of the luminous line.
The presence of even very small areas of the object's surface that reflect light in a specular manner, such as a mirror-like flat surface, can cause the reflection of a portion of the illumination light along directions that point out of the field of view of the camera. As a consequence, zones of lower brightness can be created in the images of a luminous line, these zones being potential sources of errors in the determination of the centerline. The problem can get even worse with mirror-like surface areas inadvertently oriented to reflect the illumination light right into the camera's field of view. In this situation the higher brightness of the specularly-reflected light can cause blooming of some camera pixels and then clipping of the center part of the Gaussian-shaped brightness profile along the line width. Note that fine-pitch variations of the optical reflectance are also present on the surface of an object having a nonhomogeneous composition, obtained from example by aggregating solid materials of various natures, as it is observed in many mineral rock samples. In this case, even a very fine polishing of the object surface cannot eliminate the small-scale nonuniformities in the surface reflectance.
Various methods for reducing the detrimental effects of the small-scale surface reflectance variations of the objects sensed by triangulation-based 3D profilers have been proposed in the prior art. Some techniques use a beam shaping optical element such as a holographic diffuser placed at a distance in front of the imaging sensor to redistribute and homogenize the reflected beam irradiance as it gets focused on the image sensor. The beam shaping element then serves to remove unwanted structures from the reflected light that falls on the image sensor as well as to enlarge the size of the imaged spot, thus allowing presumably more accurate estimates of the center position of the spot.
The use of a holographic optical diffuser can be thought of as an optical low-pass filtering of the reflected light before it reaches the photosensitive surface of the camera sensor. However, this low-pass filtering action can also be performed numerically on the digital images generated by the camera.
The brightness profiles along the line width are often irregular Gaussian profiles and attempting to locate the centerline by finding the position (pixel) of the maximum brightness value is not adequate for high-resolution 3D measurements. Line-splitting methods which consist in using a patterned light projector (projecting a series of parallel lines) and shifting the pattern (by a fraction of a line width) at two different positions to create slightly-displaced pairs of luminous parallel lines on the object can be used. The shift is small enough to allow the distorted Gaussian irradiance profiles along the width of both lines to partially overlap in the images formed on the camera sensor. The centerline is then located with enhanced accuracy by subtracting one profile from the other to obtain a composite brightness profile that includes both positive and negative amplitudes. The composite brightness profile also gets a null amplitude value at some pixel position, this position being used to define the centerline. The better accuracy in locating the centerline comes from the fact that the slope of the composite brightness profile at the zero-amplitude crossing point is twice that of each original Gaussian profile at this position.
Various methods for computing the centerline of a line imaged on a camera sensor are available in the prior art. Each centerline value can be accompanied by a quality factor computed to provide cues to alert a user that the data may be suspect. In a simple form, the quality factor may merely indicate whether the maximum brightness value along the line width is within acceptable levels. Alternatively, the quality factor may be an indication of the width of the Gaussian brightness profiles (relative to the pixel size) or it may quantify the degree of symmetry of the profiles. A lack of symmetry clearly indicates the presence of a corrupted Gaussian brightness profile.
By their very nature, a large proportion of the methods of the prior art developed for compensating for the detrimental effects of the small-scale variations of the surface reflectance of an object under inspection does not account for the specific way any given Gaussian brightness profile gets distorted when impinging on the object surface. In other words, several methods of the prior art process all brightness profiles in exactly the same manner, no matter the profiles may present minute distortions or large ones.
There is therefore a need for triangulation-based 3D profilers of the slit-scanner type capable of providing high-resolution measurements via appropriate compensation for the small-scale surface reflectance characteristics of an object.